Modeling states of an entity

ABSTRACT

Methods, systems and apparatus for modeling states of an entity are presented. For example, a method, implemented on a processor device, of modeling one or more states of an entity is presented. The method includes obtaining a training dataset for training a model by applying a stimulus to the entity, forming a set of model parameters, and using the set of model parameters to form the model, such that the model is configured to predict at least one of the one or more states of the entity. At least one model parameter of the set of model parameters changes with time as a result of dependency of the at least one model parameter on the stimulus and as a result of time-dependency of the stimulus. The steps of obtaining the training dataset, forming the set of model parameters and using the set of model parameters are implemented on the processor device.

FIELD OF THE INVENTION

The present invention relates generally to predictive modeling. Moreparticularly the invention relates to model learning and predictiveapplications of brain activity.

BACKGROUND OF THE INVENTION

Recent advances in medical imaging technology have introduced functionalmagnetic resonance imaging (fMRI) capable of acquiring sequences ofimages of brain activity (data) by measuring changes in bloodoxygenation levels. The acquired data may comprise a very large numberof voxels or variables taken at many points in time.

Predicting mental states, including mental disease states, is a goal ofbrain studies. Indicating current mental states or predicting futuremental states, including response to therapy, is useful in the treatmentof mental diseases.

Key challenges in the analysis of biological data, including brainrelated data, are the very high dimensionality of the data, the temporalnature of underlying processes and the complicated, and not necessarilywell understood, relationship between the environment or other stimuliand the state of the biological system, for example, the brain.

SUMMARY OF THE INVENTION

Principles of the invention provide, for example, methods, systems andapparatus for modeling states of an entity.

For example, a method, implemented on a processor device, of modelingone or more states of an entity is provided. The method includesobtaining a training dataset for training a model by applying a stimulusto the entity, forming a set of model parameters, and using the set ofmodel parameters to form the model, such that the model is configured topredict at least one of the one or more states of the entity. At leastone model parameter of the set of model parameters changes with time asa result of dependency of the at least one model parameter on thestimulus and as a result of time-dependency of the stimulus. The stepsof obtaining the training dataset, forming the set of model parametersand using the set of model parameters are implemented on the processordevice.

In accordance with another embodiment of the invention, a system,implemented on a processor device, for modeling one or more states of anentity is provided. The system comprises modules for implementing theabove method of modeling states of an entity.

In accordance with yet another embodiment of the invention, apparatusfor modeling one or more states of an entity is provided. The apparatusincludes a memory and a processor coupled to the memory. The apparatusis operative to perform the above method of modeling states of anentity.

In accordance with one more embodiment of the invention, a computerprogram product for modeling one or more states of an entity isprovided. The computer program product comprises a computer readablestorage medium having computer readable program code embodied therewith.The computer readable program code comprises computer readable programcode configured to perform the above method of modeling states of anentity.

Principles of the invention provides, for example, learning tasks,wherein a model representing fMRI data of brain scans learns parameterssuch that the model is useful in predicting mental or brain states;model parameters that evolve dynamically as functions of externaltime-dependent stimuli; efficient learning of a model that handles alarge number of voxels via application of sparse regression using theLasso method; indication of subsets of voxels or brain areas that aremost relevant to prediction of future brain states; regression modelingwith data samples that are not independent and identically distributedand form a multivariate time-series, and, using the Lasso method, treatregression parameters as time-varying random variables.

These and other features, objects and advantages of the presentinvention will become apparent from the following detailed descriptionof illustrative embodiments thereof, which is to be read in connectionwith the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a graphical representation of a regression model as adynamic Bayesian network, according to an embodiment of the presentinvention.

FIGS. 2A-2C are graphical representations comparing a regressionapproach having fixed parameters with regression approaches havingdynamic parameters, according to an embodiment of the present invention.

FIG. 3 is a flow diagram of a method for learning or forming dynamicparameters of the dynamic Lasso model, according to an embodiment of thepresent invention.

FIG. 4 depicts a computer system that may be useful in implementing oneor more aspects and/or elements of the invention.

DETAILED DESCRIPTION OF THE INVENTION

Magnetic Resonance Imaging (MRI) is an imaging technique to visualizethe internal structure and/or function of a body. MRI provides highercontrast between the different soft tissues of the body than provided bymany other imaging techniques. Consequently, MRI is useful in neurologyand brain imaging. MRI is also useful for imaging other portions of thebody, for example, musculoskeletal, cardiovascular, and for oncological(cancer) imaging. MRI does not use ionizing radiation, but uses apowerful magnetic field to align the nuclear magnetization of, forexample, hydrogen atoms in water in the body. Radio frequency (RF)fields are used to systematically alter the alignment of thismagnetization, causing the hydrogen nuclei to produce a rotatingmagnetic field detectable by the scanner. This signal can be manipulatedby additional magnetic fields to build up enough information toconstruct an image of the body or portions thereof.

Functional magnetic resonance imaging (fMRI) is a type of specializedMRI. fMRI, for example, measures the hemodynamic response (i.e.,response to the dynamic regulation of the blood flow in the brain)related to neural activity in the brain or spinal cord of humans orother animals. Neurons require energy to function. This energy issupplied in the form of glucose and oxygen carried in hemoglobin. Theblood supply of the brain is dynamically regulated to give active neuralassemblies more energy while inactive neural assemblies receive lessenergy. Therefore, changes in blood flow and blood oxygenation in thebrain (collectively known as hemodynamic) are closely linked to neuralactivity. When nerve cells are more active they consume more oxygencarried by hemoglobin in red blood cells from local capillaries. Thelocal hemodynamic response to this oxygen utilization is an increase inblood flow to regions of increased neural activity, occurring after adelay of, for example, 1-5 seconds. This local hemodynamic response mayrises to a peak over, for example, 4-5 seconds before falling back tonear baseline levels, leading to local changes in the relativeconcentration of oxyhemoglobin and deoxyhemoglobin and changes in localcerebral blood volume in addition to this change in local cerebral bloodflow. Therefore, fMRI may, for example, produce images of brain activityby measuring changes in blood oxygenation levels and/or otherhemodynamic responses.

A voxel is a volume element, representing a value, a structure or athree-dimensional image on a three-dimensional grid. A voxel isanalogous to a pixel, which represents two-dimensional image data.Voxels are frequently used in the visualization and analysis of medicaland scientific data. As with a pixel, a voxel itself typically does notcomprise spacial position or coordinates of the voxel. Rather, spacialposition of a voxel is inferred based on the position of the voxelrelative to other voxels (e.g., the position in the data structure thatmakes up a single volume image). The word voxel is a linguistic blend ofthe words volumetric and pixel.

The Least Absolute Shrinkage and Selection Operator (Lasso) method is ashrinkage and/or selection method for linear regression. The Lassomethod may minimizes the usual sum of squared errors, with a bound onthe sum of the absolute values of the coefficients. The Lasso may beassociated with soft-thresholding of wavelet coefficients, forwardstagewise regression, and boosting methods. The Lasso method isdescribed in the paper: Tibshirani, R, Regression Shrinkage andSelection via the Lasso, J. Royal. Statist. Soc B., Vol. 58, No. 1,1996, pages 267-288, the disclosure of which is incorporated herein byreference.

A Bayesian network is a probabilistic graphical model that represents aset of random variables and their conditional independencies via adirected acyclic graph (DAG). For example, a Bayesian network couldrepresent the probabilistic relationships between diseases and symptoms.Given symptoms, the network could be used to compute the probabilitiesof the presence of various diseases. Bayesian networks are DAG withnodes representing variables and missing edges representingindependencies between the variables. Nodes may represent randomvariables (i.e., random variables in a Bayesian sense) that may be, forexample, observable quantities, latent variables (variables that are notdirectly observed but are inferred, e.g., through mathematical models,from other variables that are observed or measured), unknown parametersor hypotheses. Bayesian networks that model sequences of variables(e.g., speech signals or brain activity) are called dynamic Bayesiannetworks.

A Taylor expansion or a Taylor series is a representation of a functionas an infinite sum of terms calculated from the values of itsderivatives at a single point. The Taylor series may be regarded as thelimit of the Taylor polynomials. In practice a Taylor expansion may betruncated to be of a certain order. Calculations of Taylor expansions orseries and related Taylor coefficients are well known in the art and,therefore, will not be presented herein.

A sequence or other collection of random variables is independent andidentically distributed (i.i.d.) if each random variable has the sameprobability distribution as the others and all are mutually independent.

The definition of an entity is something, living or otherwise, thatcould have its own separate and distinct existence. For example, anentity may be a brain, a person having a brain, an organism, an organismhaving a brain, or a biological system. Furthermore, an entity may benonliving, for example, a network such as a communications or datanetwork.

Exemplary embodiments of the present invention are described herein withreference to the field of fMRI to illustrate and provide a specificdomain for application of the disclosed techniques. However, embodimentsof the invention are applicable to other fields where predictivemodeling or pattern extraction is desired. Some exemplary embodiments ofthe present invention relate to brain, brain states, brain activity anddiseases of the brain. The invention is not so limited, other organs ofa body, states, activities and diseases associated with other organs ofthe body are contemplated. Where embodiments, methods and techniques ofthe invention are applied to brain or brain states, activities ordiseases, similar embodiments, methods and techniques of the inventionmay be applied to other organs or systems of the body or associatedstates, activities or diseases.

Key challenges in analysis of biological data, such as medical imaging(e.g., fMRI) include, the high dimensionality of data, the dynamic(e.g., temporal) nature of underlying processes, and the complicatedrelationship between different stimuli and a ‘state of the biologicalsystem’ that need to be modeled.

Embodiments of the invention are useful, for example, in processinglarge amounts of data, such as data produced in conjunction with oranalysis of functional magnetic resonance imaging (fMRI). fMRImeasurements can give rise to large amounts of data, for example,consisting of tens of thousands or hundreds of thousands of voxelsand/or hundreds or thousands of samples, for example, time points orsamples.

According to aspects of the invention, fMRI may be used to scan thebrains of subjects, for example, while the brains are receiving stimulior when brains are diseased or have other states. Embodiments of theinvention provide for learning tasks, wherein a model representing fMRIdata of brain scans learns (forms) parameters such that the model isuseful in predicting mental or brain states.

According to aspects of the invention, fMRI data (e.g., time-series datacollected at each voxel) may be used to predict the brain, mental orcognitive state of a subject, for example, an emotion (e.g., anger,happiness, sadness, anxiousness, or annoyance); extract patterns of orpredict a mental disease, for example, schizophrenia, depression,Alzheimer's or dementia; discriminate between mental or brain states ofa person, for example brain or mental states associated with a personlooking at a face or at a building, a person listening to a phrase in afirst language or a phrase in a second language, a person performing amental or physical task or different mental or physical tasks, or aperson having one or other emotion; and predicting brain activity givena specific stimulus or specific stimuli (e.g., auditory such as words orsounds, visual such as pictures, or activity of a person such as playinga video-game).

The term brain state, as used herein, comprises the mental or cognitivestate of a subject, a mental disease state, a brain response to astimulus, a brain response to a physical or mental task, and any otherstate related to the brain that is discernable using measurementtechniques (e.g. fMRI) of the invention.

As an example of an embodiment of the invention, consider a training ofa model and subsequent perdition by the model. The training comprisesthree runs through a virtual reality sequence or video game. fMRI datais obtained from each run, for example, continuous or periodic snapshotfMRI data. Each run is rated on a number of features, for example,continuous features, subjective features (annoyance, sadness andanxiety), and objective features (presentation of objects orrepresentation of objects such as a dog, presentation of visual stimulisuch as faces, presentation and/or fulfillment of instructions, andsuccessful completion of tasks or successful responses). After thetraining, the model is useful in predicting brain or mental states, suchas those mentioned above. The training may be performed using dataobtained from the same or different subject as the subject undergoingthe prediction process (i.e., test subjects). The trained model modelsbrain or mental states of the training subjects or other test subjects.

Aspects of the invention include, for example, a general framework formodeling stimuli-dependent (i.e., context-specific) dynamics of brain.Dependencies between voxels at different time-slices may be modeled, forexample, using a dynamic Bayesian network (DBN) model, wheredependencies among random variables/voxels follow linear Gaussianmodels.

An exemplary advantage of the invention is that parameters of the modelare not fixed (e.g., parameters in relationship to fMRI, and inrelationship to machine-learning using DBNs), but evolve dynamically asfunctions of external stimuli.

A model, according to an embodiment of the invention, combinesunderlying brain dynamics with stimuli-related brain dynamics in onemodel. An exemplary method of the invention for learning or forming sucha model may be very efficient and may handle a large number (e.g.,hundreds of thousands) of voxels or dimensions via application of sparseregression (i.e., a regression using a parsimonious subset of allavailable repressors for an efficient prediction of a target variable)using the Lasso method or extensions of Lasso methods, e.g., an elasticnetwork method. The elastic network method is known in the art anddescribed in the paper: Zou, H. and Hastie, T.; Regularization andVariable Selection via the Elastic-net; J. R. Statist. Soc. B 2005; vol.67, pages 301-320, the disclosure of which is incorporated herein byreference. The elastic net or elastic network is a regularization andvariable selection method. The elastic net encourages a grouping effect,where strongly correlated predictors tend to be in or out of anassociated model together. The elastic net is particularly useful whenthe number of predictors is much bigger than the number of observations.A least angle regression selection-elastic net (LARS-EN) algorithm cancompute elastic net regularization paths efficiently, much like a leastangle regression selection (LARS) method or algorithm does for theLARS-EN regression. The LARS method is known in the art and described inthe paper: Efron, B., et al.; Least Angular Regression; the Annals ofStatistics 2004; vol. 32, No. 2, pages 407-499, the disclosure of whichis incorporated herein by reference. LARS is a linear model selectionalgorithm. A LARS algorithm may implement the Lasso method. A LARSalgorithm may implement forward stagewise linear regression and use apiecewise linear solution path using a modification of forward stagewiseand least angle regression paths. An exemplary advantage of LARS isshort computation.

Another exemplary advantage of the invention is interpretability andpredictions of the dynamical model that results from application ofsparse regression. The model indicates which subsets of voxels or brainareas are most relevant to prediction of the future brain states and/orother variables (e.g., mental states and/or variables associated with:mental, emotional or cognitive states; sensory or other stimulus, e.g.,viewing a particular image; or having a certain mental illness).

Exemplary methods of the invention also advance sparse regressionmethodology by providing learning or forming of dynamically changingsubsets of relevant variables, unlike some Lasso and Elastic Networkmethodologies.

Aspects of the invention consider, for example, regression problems withsamples that are not independent and identically distributed (non-i.i.d.samples) that form a multivariate time-series (i.e., a time-seriescomprising or involving a number of independent mathematical orstatistical variables) and use an extension of standard sparseregression methods, for example, the Lasso method, by treating theregression parameters as time-varying random variables. This approach isapplied, for example, to the task of predicting brain or mental statesfrom fMRI data.

Advantages of the invention include, for example, a dynamic model thattreats fMRI data as a real time-series rather than i.i.d. samples, andallows for dynamically changing parameters as functions of stimuli,other environmental conditions and conditions that are inherent tobrain, i.e. allows for a context-specific model of overall brainactivity, thus providing a flexible and realistic way of modeling brain.Advantages of the invention also include, for example, efficiency andpracticality due to use of sparse regression techniques such as Lassothat provide for high-dimensional time-series. Moreover, sparse modelsprovide for interpretability because sparse models select subsets ofvariables (voxels) from the past most relevant to prediction of brainactivity in the future. Further advantages of the invention include, forexample, the stimuli-dependent adaptation of sparse selection providingfor identifying specific brain areas that are most predictive of futureactivity under specific stimuli, rather than trying to learn usingstimuli-independent models.

The following regression model is used where the coefficients β_(ij) arenot fixed, but are dynamic functions of the stimuli y: x_(i)^(t+1)=β_(i0)(y^(t))+β_(i1)(y^(t))x₁ ^(t)+ . . . +β_(ip)(y^(t))x_(p)^(t)

An exemplary graphical representation 100 of the above regression modelas a dynamic Bayesian network is shown in FIG. 1, where theindependencies, dependencies and relationships between the stimuli 110and the predictors 120 are not identified as indicated by the indicator130. In FIGS. 1, 2A, 2B, 2C and 3 and in the text of the specificationthe variable “x” has the same meaning as “X” and the variable “y” hasthe same meaning as “Y”.

FIGS. 2A, 2B and 2C compare a regression approach having fixed (e.g.,not stimulus and not time dependent) parameters β with a dynamicregression method of the invention. FIG. 2A is a graph 210 illustratinga linear regression with fixed parameters β. FIG. 2A may represent, forexample, a noisy linear model with fixed parameters β as expressed bythe equation below.x _(i) ^(t+1)=β_(i0)+β_(i1) x ₁ ^(t)+ . . . +β_(ip) x _(p) ^(t)+noise

Using the Lasso method (maximum likelihood (min−log-likelihood)) withGaussian noise and prior Laplace transformation on parameters β:

${\min_{\beta_{i}}{\sum\limits_{t}\left( {x_{i}^{t} - {X^{t - 1}\beta}} \right)^{2}}} + {\lambda{\sum\limits_{j = 1}^{p}{\beta_{ij}}}}$As the graph 210 shows, X^(t) is calculated using X^(t−1) and β.

FIG. 2B is a graph 220 illustrating a dynamic regression with dynamicparameters, according to an embodiment of the invention. Graph 220 ofFIG. 2B may represent, for example, a noisy linear model with dynamicparameters β as a function y^(t), i.e., β(y^(t)), expressed by theregression equation below (equation 2B-1). The dynamic parameters β,besides being expressed as β(y^(t)), may also be expressed as β^(t) orβ(y^(t)). The dynamic parameters β are coefficients of the regression.x _(i) ^(t+1)=β_(i0)(y ^(t))+β_(i1)(y ^(t))x ₁ ^(t)+ . . . +β_(ip)(y^(t))x _(p) ^(t)+noise  Equation 2B-1:

The dynamic parameters β may be dynamically changing as a function oftime t and/or y. For example, the dynamic parameters β may be anarbitrary function of y. For another example, the dynamic parameter βmay be represented by a Taylor expansion function (Taylor series) of yas shown in the equation below (equation 2B-2) for dynamic parametersβ_(ij)(y).β_(ij)(y)=α_(0ij)+α_(1ij) y+α _(2ij) y ²+  Equation 2B-2:The Taylor expansion may be of any order. α_(0ij), α_(1ij), α_(2ij) andother higher order coefficients (α_(kij)) are the coefficients of theTaylor expansion. Calculation of the coefficients of the Taylorexpansion is well known in the art and, therefore, will not be presentedherein.

Substituting β_(ij)(y) form the above equation (equation 2B-2) intoequation 2B-1, equation 2B-3 is derived.

$\begin{matrix}{x_{i}^{t + 1} = {\alpha_{0i\; 0} + {\alpha_{0\; i\; 1}x_{1}^{t}} + \ldots + {\alpha_{0\;{ip}}x_{p}^{t}} + {\alpha_{1i\; 0}y} + {\alpha_{1i\; 1}{yx}_{1}^{t}} + \ldots + {\alpha_{0\;{ip}}{yx}_{p}^{t}} + \ldots + {noise}}} & {{Equation}\mspace{14mu} 2B\text{-}3}\end{matrix}$

Graph 220 and Equation 2B-3 may represent, model or be associated with,for example, a multivariate time-series, a regression with non-i.i.d.samples, the Lasso method, and/or regression parameters consideredtime-varying and/or random variables. This approach may be applied, forexample, to the task of predicting brain or mental states from fMRIdata. Equation 2B-3 may model, for example, stimuli-dependent and/ortime-dependent brain dynamics.

FIG. 2C is a graph 230 illustrating a dynamic Bayesian network withdynamic Lasso regression, according to an embodiment of the invention.X^(t) represents voxels and y represents the stimuli. Graph 230 showsthat the dynamic parameter β^(t−1) is dependent upon or is a function ofY^(t−1). Similarly, graph 230 also shows that the dynamic parameterβ^(t) is dependent upon or is a function of Y^(t). Graph 230 also showsthat X^(t−1) is dependent upon or is a function of β^(t−1), and thatX^(t) is dependent upon or is a function of fit. Furthermore, graph 230shows that Y^(t) is dependent upon or is a function of Y^(t−1), and thatX^(t) is dependent upon or is a function of X^(t−1).

The dynamic parameters β change with time (i.e., are time-dependent)resulting from dependency of the dynamic parameters β on y (i.e., thestimuli) and the time-dependency of y.

FIG. 3 is a flow diagram of a method 300 for learning or forming dynamicparameters β of the dynamic Lasso model, according to an embodiment ofthe invention. Once the dynamic parameters are learned, the dynamicparameters are inserted into the equations of the Lasso model to form acompleted Lasso model. Steps of method 300 are shown in an exemplaryorder. The method may comprise the steps in the shown order or indifferent orders. Each of the steps may occur one or more times.

The first step 301 of method 300 is obtaining a data matrix X ofdimensions N and D (i.e., N×D), where N is the number of time samplesand D is the dimensionality of each time sample. For example, the datamatrix X has N rows and D columns. In a model learning embodiment of theinvention, the data matrix X is a training dataset for learning thedynamic parameters β of the model.

By way of example, the data matrix X may comprise fMRI brain scanmultivariate time-series data which represent brain states or brainactivity. The data matrix X may be produced in response to a stimulus orstimuli. Again by way of example, the stimulus or stimuli may comprisesensory stimulus (e.g., viewing a particular image, smelling aparticular odor, hearing a particular sound, tasting a particularflavor, or touching a particular texture, shape or object), performing aparticular mental or physical task, having a certain mental illness, orstimulus evoking a particular emotion. In the training embodiment, thestimulus or stimuli is applied to a training entity. In the aboveexample, the training entity may be, for example, a brain or a personhaving the brain.

The stimuli may be represented by a vector Y of size N×1, e.g., a singlerow having N entries.

The second step 302 is to form a Taylor expansion of order m for thedynamic parameters β. The order m of the Taylor expansion may, forexample, be chosen arbitrarily or from prior experience. For Taylorexpansions having lower orders m, less computation is required.Generally, the higher the order m is, the greater the accuracy of therepresentation of the dynamic parameters β by the Taylor expansion. Inorder to minimize computation, a relatively low order m may be initiallychosen.

The third step 303 is, for the data matrix X, to learn or form thedynamic parameters β for the model of the dynamic Lasso method (i.e.,the Lasso model). The dynamic parameters β may be learned by, forexample, LARS, for example, using interactive variable selection. Thedynamic parameters β may be, for example, a function of y^(t), i.e.,β(y^(t)). One or more of the dynamic parameters β, for example, may belearned for each time sample and/or for each dimension of data matrix X.The dynamic parameter β may be represented by a Taylor expansion of y asshown in the equation 2B-2 for dynamic parameters β_(ij)(y), where yrepresents stimulus or stimuli. The learned dynamic parameters β are, atleast temporarily, inserted into a portion of the Lasso model (i.e.,that portion of the Lasso model that does not include the learnedparameters β) to form an unverified model.

The fourth step 304 is to test the Lasso model having the learneddynamic parameters β represented by a Taylor expansion of order m. Inparticular, the accuracy of the Taylor expansion of order m may betested. Training data may be used, for example, to test the Lasso model.The Lasso model is applied to the training dataset and stimulus orstimuli to produce or form an accuracy indicator. For example,considering equations 2B-1, 2B-2 and 2B-3, the training data correspondsto x_(i) ^(t+1), x₁ ^(t), . . . and x_(p) ^(t), the stimuli correspondsto y, and the parameters β correspond to βij(y) given by the Taylorexpansion βij(y)=α_(0ij)+α_(1ij) y+α_(2ij)y²+ . . . . The accuracyindicator reflects, for example, the accuracy of equation 2B-1 or 2B-3and is a measure of the accuracy of the Taylor expansion 2B-2. Theaccuracy of the Taylor expansion may be improved by adding higher orderterms.

The fifth step 305 determines if a predetermined accuracy has beenachieved by comparing the accuracy indicator to the predeterminedaccuracy threshold. The predetermined accuracy may be a desired accuracythat was previously determined. If the predetermined accuracy isachieved with the learned dynamic parameters β represented by a Taylorexpansion of order m, the dynamic parameters are accepted and returnedto the Lasso model at a seventh step 307. The method 300 terminates atthe seventh step 307.

Returning the model parameters at the seventh step 307 may be consideredthe final step in forming the model, for example, by providing necessaryinformation to the model. The completed Lasso model is formed byinserting the dynamic parameters into the incomplete Lasso model (i.e.,the Lasso model without the returned parameters). As an example, aregression model (i.e., a completed or entire regression model) isformed by inserting the learned regression parameters into theregression equation(s). The regression equation without the learnedregression parameters is considered a partial or incomplete model. Byway of example only, equation 2B-1 is considered a partial or incompletemodel when the dynamic parameters β_(ij) are unknown. Once the dynamicparameters β_(ij) are learned or known (i.e., α_(0ij), α_(1ij) andα_(2ij) are known) according to equation 2B-2, and the dynamicparameters β_(ij) are inserted into equation 2B-1, the model iscomplete.

If the predetermined accuracy is not achieved with the learned dynamicparameters β represented by a Taylor expansion of order m, one or morehigher-order terms are added to the Taylor expansion at the sixth step306. At the sixth step 306, the order m of the Taylor expansion for thedynamic parameters β is increased by an integer n (m=m+n). n may be, forexample, the integer one (1) or an integer greater than one. A newTaylor expansion of this higher order is thus formed. The new higherorder becomes the order m of the new Taylor expansion. Increasing theorder m of the Taylor expansion is an example of increasing a complexityof the model by increasing a complexity of a dependence of anautoregressive parameter on the stimulus.

After the sixth step 306, the method 300 then returns to the third step303. Method 300 continues in this manner until the predeterminedaccuracy is achieved or the method 300 is otherwise terminated. When thepredetermined accuracy is achieved, as indicated by the accuracyindicator at or above the predetermined accuracy threshold, theresulting Lasso model comprising the dynamic parameters β represented bythe Taylor expansion of final order m is considered to be the verifiedLasso model.

The verified Lasso model, or other model, may be applied to a testdataset, obtained by applying the stimulus or stimuli to a test entity,and thus used to predict a mental state of the test entity. In anembodiment of the invention, the stimulus or stimuli applied to the testentity is the same or similar stimulus or stimuli that were applied tothe training entity to obtain the training dataset (i.e., data matrix X)in step 301 of method 300. The test entity may be the same as thetraining entity or different than the training entity.

By way of example, the test dataset may comprise fMRI brain scanmultivariate time-series data which represent brain states or brainactivity of the test entity, and the stimulus or stimuli may comprisesensory stimulus, performance by the test entity of a particular mentalor physical task, having a certain mental illness, or stimulus evoking aparticular emotion. The test entity may be, for example, a brain or aperson having the brain.

A feature of the proposed method that justifies the term “dynamic Lasso”is that sparsity-enforcing L1-regularization (Lebesgue1-regularization)is added to the regression, like in the non-dynamic Lasso, but incombination with the stimuli-dependent coefficients.

In general, it is assumed that the Taylor expansion described above onlyincludes the elements up to an order m, i.e. α_(kij)=0 for k>m. In orderto find the parameters of the dynamic Lasso model described above, thefollowing L1-regularized likelihood-maximization problem is solved:

$\begin{matrix}{{\max\limits_{\alpha}{P\left( {\left. \alpha \middle| X \right.,Y} \right)}} = {\min\limits_{\alpha}\left\lbrack {{- \log}\;{P\left( X \middle| \alpha \right)}{P(\alpha)}{P(Y)}} \right\rbrack}} \\{= {{\sum\limits_{t = 2}^{n}{\sum\limits_{i = 1}^{p}\left( {x_{i}^{t} - {\sum\limits_{k = 0}^{m}{\sum\limits_{j = 1}^{p}{{\alpha_{kij}\left( y^{t - 1} \right)}^{k}x_{j}^{t - 1}}}}} \right)^{2}}} +}} \\{\underset{i}{\overset{p}{\lambda\sum}}{\sum\limits_{k = 0}^{m}{\sum\limits_{j = 1}^{p}{\alpha_{kij}}}}} \\{= {\sum\limits_{i = 1}^{p}\left\lbrack {{\sum\limits_{t = 2}^{n}\left( {x_{i}^{t} - {\sum\limits_{k = 0}^{m}{\sum\limits_{j = 1}^{p}{{\alpha_{kij}\left( y^{t - 1} \right)}^{k}x_{j}^{t - 1}}}}} \right)^{2}} +} \right.}} \\{\lambda{\sum\limits_{k = 0}^{m}{\sum\limits_{j = 1}^{p}{\alpha_{kij}}}}}\end{matrix}$

Herein it is assumed that the data X follow the linear Gaussian model,i.e. that P(X|α) is a joint Gaussian distribution of a vector ofindependent Gaussian variables x_(i) ^(t), with unit variance, and thatmean P(α) is a Laplace distribution (prior) λ e^(λ|α)kij^(|) with afixed constant hyper-parameter λ. Note that P(Y), the prior on Y, doesnot depend on the vector of parameters, α, and thus can be ignored inthe above optimization problem.

As will be appreciated by one skilled in the art, aspects of the presentinvention may be embodied as a system, method or computer programproduct. Accordingly, aspects of the present invention may take the formof an entirely hardware embodiment, an entirely software embodiment(including firmware, resident software, micro-code, etc.) or anembodiment combining software and hardware aspects that may allgenerally be referred to herein as a “circuit,” “module” or “system.”Furthermore, aspects of the present invention may take the form of acomputer program product embodied in one or more computer readablemedium(s) having computer readable program code embodied thereon.

Any combination of one or more computer readable medium(s) may beutilized. The computer readable medium may be a computer readable signalmedium or a computer readable storage medium. A computer readablestorage medium may be, for example, but not limited to, an electronic,magnetic, optical, electromagnetic, infrared, or semiconductor system,apparatus, or device, or any suitable combination of the foregoing. Morespecific examples (a non-exhaustive list) of the computer readablestorage medium would include the following: an electrical connectionhaving one or more wires, a portable computer diskette, a hard disk, arandom access memory (RAM), a read-only memory (ROM), an erasableprogrammable read-only memory (EPROM or Flash memory), an optical fiber,a portable compact disc read-only memory (CD-ROM), an optical storagedevice, a magnetic storage device, or any suitable combination of theforegoing. In the context of this document, a computer readable storagemedium may be any tangible medium that can contain, or store a programfor use by or in connection with an instruction execution system,apparatus, or device.

A computer readable signal medium may include a propagated data signalwith computer readable program code embodied therein, for example, inbaseband or as part of a carrier wave. Such a propagated signal may takeany of a variety of forms, including, but not limited to,electro-magnetic, optical, or any suitable combination thereof. Acomputer readable signal medium may be any computer readable medium thatis not a computer readable storage medium and that can communicate,propagate, or transport a program for use by or in connection with aninstruction execution system, apparatus, or device.

Program code embodied on a computer readable medium may be transmittedusing any appropriate medium, including but not limited to wireless,wireline, optical fiber cable, RF, etc., or any suitable combination ofthe foregoing.

Computer program code for carrying out operations for aspects of thepresent invention may be written in any combination of one or moreprogramming languages, including an object oriented programming languagesuch as Java, Smalltalk, C++ or the like and conventional proceduralprogramming languages, such as the “C” programming language or similarprogramming languages. The program code may execute entirely on theuser's computer, partly on the user's computer, as a stand-alonesoftware package, partly on the user's computer and partly on a remotecomputer or entirely on the remote computer or server. In the latterscenario, the remote computer may be connected to the user's computerthrough any type of network, including a local area network (LAN) or awide area network (WAN), or the connection may be made to an externalcomputer (for example, through the Internet using an Internet ServiceProvider).

Aspects of the present invention are described below with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems) and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer program instructions. These computer program instructions maybe provided to a processor of a general purpose computer, specialpurpose computer, or other programmable data processing apparatus toproduce a machine, such that the instructions, which execute via theprocessor of the computer or other programmable data processingapparatus, create means for implementing the functions/acts specified inthe flowchart and/or block diagram block or blocks.

These computer program instructions may also be stored in a computerreadable medium that can direct a computer, other programmable dataprocessing apparatus, or other devices to function in a particularmanner, such that the instructions stored in the computer readablemedium produce an article of manufacture including instructions whichimplement the function/act specified in the flowchart and/or blockdiagram block or blocks.

The computer program instructions may also be loaded onto a computer,other programmable data processing apparatus, or other devices to causea series of operational steps to be performed on the computer, otherprogrammable apparatus or other devices to produce a computerimplemented process such that the instructions which execute on thecomputer or other programmable apparatus provide processes forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks.

Referring again to FIG. 3, which is a flow diagram or flowchart of themethod 300, the flowchart and block diagrams in the Figure illustratethe architecture, functionality, and operation of possibleimplementations of systems, methods and computer program productsaccording to various embodiments of the present invention. In thisregard, each block in the flowchart or block diagrams may represent amodule, segment, or portion of code, which comprises one or moreexecutable instructions for implementing the specified logicalfunction(s). It should also be noted that, in some alternativeimplementations, the functions noted in the block may occur out of theorder noted in the figures. For example, two blocks shown in successionmay, in fact, be executed substantially concurrently, or the blocks maysometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts, or combinations of special purpose hardware andcomputer instructions.

Accordingly, techniques of the invention, for example as depicted inFIGS. 1-4, can also include, as described herein, providing a system,wherein the system includes distinct software modules. By way of exampleonly, the software modules may include: a training data procurementmodule, a parameter forming module, a model forming module, a trainingapplication module, a comparison module, an accuracy module, a test dataprocurement module and a prediction module. The modules may be adapted,for example, to perform the steps of method 300 illustrated in FIG. 3.

Specifically, the training data procurement module is adapted to obtaina training dataset for training the model by applying a stimulus (orstimuli) to a training entity. The parameter forming module is adaptedto form the set of model parameters. The model parameters change withtime resulting from dependency of the model parameters on the stimulus(or stimuli) and the time-dependency of the stimulus (or stimuli). Themodel forming module is adapted to form the model by inserting theformed set of model parameters into at least a portion of the model. Thetraining application module is adapted to apply the model to thetraining dataset to produce an accuracy indicator for verifying themodel. The comparison module is adapted to compare the accuracyindicator with a predetermined accuracy threshold. The accuracy moduleis adapted to increase a complexity of the model by increasing acomplexity of a dependence of an autoregressive parameter on thestimulus (or stimuli) when the accuracy indicator is below thepredetermined accuracy threshold. The test data procurement module isadapted to obtain a test dataset by applying the stimulus (or stimuli)to a test entity. The prediction module is adapted to predict a mentalstate by applying the model to the test dataset and the stimulus (orstimuli).

One or more embodiments can make use of software running on a generalpurpose computer or workstation. With reference to FIG. 4, such animplementation employs, for example, a processor 402, a memory 404, andan input/output interface formed, for example, by a display 406 and akeyboard 408. The term “processor” as used herein is intended to includeany processing device, such as, for example, one that includes a CPU(central processing unit) and/or other forms of processing circuitry.Further, the term “processor” may refer to more than one individualprocessor. The term “memory” is intended to include memory associatedwith a processor or CPU, such as, for example, RAM (random accessmemory), ROM (read only memory), a fixed memory device (for example,hard drive), a removable memory device (for example, diskette), a flashmemory and the like. In addition, the phrase “input/output interface” asused herein, is intended to include, for example, one or more mechanismsfor inputting data to the processing unit (for example, keyboard ormouse), and one or more mechanisms for providing results associated withthe processing unit (for example, display or printer). The processor402, memory 404, and input/output interface such as display 406 andkeyboard 408 can be interconnected, for example, via bus 410 as part ofa data processing unit 412. Suitable interconnections, for example viabus 410, can also be provided to a network interface 414, such as anetwork card, which can be provided to interface with a computernetwork, and to a media interface 416, such as a diskette or CD-ROMdrive, which can be provided to interface with media 418.

A data processing system suitable for storing and/or executing programcode can include at least one processor 402 coupled directly orindirectly to memory elements 404 through a system bus 410. The memoryelements can include local memory employed during actual execution ofthe program code, bulk storage, and cache memories which providetemporary storage of at least some program code in order to reduce thenumber of times code must be retrieved from bulk storage duringexecution.

Input/output or I/O devices (including but not limited to keyboard 408,display 406, pointing device, and the like) can be coupled to the systemeither directly (such as via bus 410) or through intervening I/Ocontrollers (omitted for clarity).

Network adapters such as network interface 414 may also be coupled tothe system to enable the data processing system to become coupled toother data processing systems or remote printers or storage devicesthrough intervening private or public networks. Modems, cable modem andEthernet cards are just a few of the currently available types ofnetwork adapters.

As used herein, including the claims, a “server” includes a physicaldata processing system (for example, system 412 as shown in FIG. 4)running a server program. It will be understood that such a physicalserver may or may not include a display and keyboard.

It will be appreciated and should be understood that the exemplaryembodiments of the invention described above can be implemented in anumber of different fashions. Given the teachings of the inventionprovided herein, one of ordinary skill in the related art will be ableto contemplate other implementations of the invention. Indeed, althoughillustrative embodiments of the present invention have been describedherein with reference to the accompanying drawings, it is to beunderstood that the invention is not limited to those preciseembodiments, and that various other changes and modifications may bemade by one skilled in the art without departing from the scope orspirit of the invention.

What is claimed is:
 1. A method comprising the steps of: constructing afirst model which represents a pattern of neural activity that occurs inregions of a human brain in response to a first type of stimulus appliedto the human brain, wherein the first model represents a brain state ofa human as a function of the first type of stimulus applied to the humanbrain, wherein constructing the first model comprises: scanning thebrains of a plurality of test subjects using functional magneticresonance imaging (fMRI) to obtain a training dataset of fMRI data whilethe first type of stimulus is being applied to the brains of the testsubjects, wherein the training dataset of fMRI data represents neuralactivity in regions of the brains of the test subjects in response toapplied stimulus; processing the training dataset of fMRI data to form aset of model parameters, wherein at least one model parameter of the setof model parameters is a dynamic model parameter, wherein the dynamicmodel parameter is defined as a dynamic function of an applied stimulussuch that the dynamic model parameter changes based on a type of theapplied stimulus, wherein the dynamic model parameter is trained basedon a type of the applied stimulus used to obtain the training dataset offMRI data, wherein the dynamic model parameter comprises at least onecoefficient that dynamically changes with time based on (i) a dependencyof the dynamic model parameter on the type of the applied stimulus and(ii) a time-dependency of the applied stimulus; using the set of modelparameters to form the first model, such that the first model isconfigured to represent which regions of a human brain are mostpredictive of at least one or more stimuli-dependent brain states of thehuman brain; wherein the model comprises a regression comprisingcoefficients, wherein the coefficients of the regression are dependentupon the stimulus and expressed as a Taylor expansion of the stimulus,wherein the coefficients of the regression are dynamic model parametersof the set of model parameters, wherein the dynamic model parameters areindicated by βij(y) and expressed as:βij(y)=α_(0ij)+α_(1ij) y+α _(2ij) y ²+ . . . ; wherein y represents thestimulus; and wherein α_(0ij), α_(1ij), and α_(2ij) are coefficients ofthe Taylor expansion and i and j are indexes of the parameters;utilizing the first model to determine a brain state of an individual,wherein utilizing the model comprises: acquiring a test dataset of fMRIdata for the individual by (i) applying the first type of stimulus tothe brain of the individual and (ii) obtaining fMRI data measurementsfrom the brain of the individual in response to the applied stimulus;and applying the acquired test dataset of fMRI data of the individual tothe first model to determine a subset of voxels of the first model whichis selected in response to the acquired test dataset of fMRI data,wherein the subset of voxels corresponds to a specific region of thehuman brain; determining that the individual has a brain state whichcorresponds to the human brain state represented by the first model,when the selected subset of voxels of the first model corresponds to anexpected subset of voxels of the first model which would be expected tobe selected in response to the applied test dataset of fMRI data if theindividual had said brain represented by the first model; wherein thehuman brain state represented by the first model comprises at least oneof a cognitive state and a mental disease state; and constructing asecond model which represents a pattern of neural activity that occursin regions of a human brain in response to a second type of stimulusapplied to the human brain, wherein second model represents a brainstate of a human as a function of the second type of stimulus applied tothe human brain, wherein the second model is constructed by dynamicallyadjusting the at least one dynamic model parameter of the set of modelparameters used to form the first model using a second training datasetof fMRI data which is acquired with the second type of stimulus beingapplied to the brains of the test subjects; wherein the method steps areperformed by a processor device executing program instructions.
 2. Themethod of claim 1, wherein forming the set of model parameters comprisesapplying at least one of: (i) a Lasso method, (ii) an elastic networkmethod, (iii) a least angle regression selection-elastic network method,and (iv) a least angle regression selection method.
 3. The method ofclaim 1 further comprising the steps of: verifying an accuracy of thefirst model by applying the first model to the training dataset todetermine level of accuracy of the first model predicting the humanbrain state represented by the first model; comparing the determinedlevel of accuracy with a predetermined accuracy threshold; andincreasing a complexity of the first model by increasing a complexity ofa dependence of an autoregressive parameter on the stimulus when thedetermined level of accuracy is below the predetermined accuracythreshold.
 4. The method of claim 3, wherein one or more of the steps offorming the set of model parameters, using the set of model parametersto form the first model, comparing the determined level of accuracy withthe predetermined accuracy threshold, and increasing a complexity of thefirst model, are repeated until the determined level of accuracy is atleast one of equal to the predetermined accuracy threshold and above thepredetermined accuracy threshold.
 5. The method of claim 1, whereinapplying the acquired test dataset of fMRI data of the individual to thefirst model to determine a subset of voxels of the first model which isselected in response to the acquired test dataset of fMRI data comprisesapplying at least one of: (i) a Lasso method, (ii) an elastic networkmethod, (iii) a least angle regression selection-elastic network method,and (iv) a least angle regression selection method.
 6. The method ofclaim 3, wherein increasing a complexity of the first model comprisesadding at least one additional regression coefficient.
 7. The method ofclaim 6, wherein adding the at least one additional regressioncoefficient comprises adding at least one higher order regressioncoefficient to the Taylor expansion.
 8. A computer program productcomprising a computer readable storage medium having computer readableprogram code embodied therewith, the computer readable program codecomprising computer readable program code configured to perform thesteps of: constructing a first model which represents a pattern ofneural activity that occurs in regions of a human brain in response to afirst type of stimulus applied to the human brain, wherein the firstmodel represents a brain state of a human as a function of the firsttype of stimulus applied to the human brain, wherein constructing thefirst model comprises: scanning the brains of a plurality of testsubjects using functional magnetic resonance imaging (fMRI) to obtain atraining dataset of fMRI data while the first type of stimulus is beingapplied to the brains of the test subjects, wherein the training datasetof fMRI data represents neural activity in regions of the brains of thetest subjects in response to applied stimulus; processing the trainingdataset of fMRI data to form a set of model parameters, wherein at leastone model parameter of the set of model parameters is a dynamic modelparameter, wherein the dynamic model parameter is defined as a dynamicfunction of an applied stimulus such that the dynamic model parameterchanges based on a type of the applied stimulus, wherein the dynamicmodel parameter is trained based on a type of the applied stimulus usedto obtain the training dataset of fMRI data, wherein the dynamic modelparameter comprises at least one coefficient that dynamically changeswith time based on (i) a dependency of the dynamic model parameter onthe type of the applied stimulus and (ii) a time-dependency of theapplied stimulus; using the set of model parameters to form the firstmodel, such that the first model is configured to represent whichregions of a human brain are most predictive of at least one or morestimuli-dependent brain states of the human brain; wherein the modelcomprises a regression comprising coefficients, wherein the coefficientsof the regression are dependent upon the stimulus and expressed as aTaylor expansion of the stimulus, wherein the coefficients of theregression are dynamic model parameters of the set of model parameters,wherein the dynamic model parameters are indicated by βij(y) andexpressed as:βij(y)=α_(0ij)+α_(1ij) y+α _(2ij) y ²+ . . . ; wherein y represents thestimulus; and wherein α_(0ij), α_(1ij), and α_(2ij) are coefficients ofthe Taylor expansion and i and j are indexes of the parameters;utilizing the first model to determine a brain state of an individual,wherein utilizing the model comprises: acquiring a test dataset of fMRIdata for the individual by (i) applying the first type of stimulus tothe brain of the individual and (ii) obtaining fMRI data measurementsfrom the brain of the individual in response to the applied stimulus;and applying the acquired test dataset of fMRI data of the individual tothe first model to determine a subset of voxels of the first model whichis selected in response to the acquired test dataset of fMRI data,wherein the subset of voxels corresponds to a specific region of thehuman brain; determining that the individual has a brain state whichcorresponds to the human brain state represented by the first model,when the selected subset of voxels of the first model corresponds to anexpected subset of voxels of the first model which would be expected tobe selected in response to the applied test dataset of fMRI data if theindividual had said brain represented by the first model; wherein thehuman brain state represented by the first model comprises at least oneof a cognitive state and a mental disease state; and constructing asecond model which represents a pattern of neural activity that occursin regions of a human brain in response to a second type of stimulusapplied to the human brain, wherein second model represents a brainstate of a human as a function of the second type of stimulus applied tothe human brain, wherein the second model is constructed by dynamicallyadjusting the at least one dynamic model parameter of the set of modelparameters used to form the first model using a second training datasetof fMRI data which is acquired with the second type of stimulus beingapplied to the brains of the test subjects.
 9. The computer programproduct of claim 8, wherein forming the set of model parameterscomprises applying at least one of: (i) a Lasso method, (ii) an elasticnetwork method, (iii) a least angle regression selection-elastic networkmethod, and (iv) a least angle regression selection method.
 10. Thecomputer program product of claim 8, further comprising the steps of:verifying an accuracy of the first model by applying the first model tothe training dataset to determine level of accuracy of the first modelpredicting the human brain state represented by the first model;comparing the determined level of accuracy with a predetermined accuracythreshold; and increasing a complexity of the first model by increasinga complexity of a dependence of an autoregressive parameter on thestimulus when the determined level of accuracy is below thepredetermined accuracy threshold.
 11. The computer program product ofclaim 10, wherein one or more of the steps of forming the set of modelparameters, using the set of model parameters to form the first model,comparing the determined level of accuracy with the predeterminedaccuracy threshold, and increasing a complexity of the first model, arerepeated until the determined level f accuracy is at least one of equalto the predetermined accuracy threshold and above the predeterminedaccuracy threshold.
 12. The computer program product of claim 8, whereinapplying the acquired test dataset of fMRI data of the individual to thefirst model to determine a subset of voxels of the first model which isselected in response to the acquired test dataset of fMRI data comprisesapplying at least one of: (i) a Lasso method, (ii) an elastic networkmethod, (iii) a least angle regression selection-elastic network method,and (iv) a least angle regression selection method.
 13. The computerprogram product of claim 10, wherein increasing a complexity of thefirst model comprises adding at least one additional regressioncoefficient.
 14. The computer program product of claim 13, whereinadding the at least one additional regression coefficient comprisesadding at least one higher order regression coefficient to the Taylorexpansion.
 15. Apparatus comprising: a memory configured to storeprogram instructions; and a processor coupled to the memory, operativeto process the stored program instructions to implement a processcomprising: constructing a first model which represents a pattern ofneural activity that occurs in regions of a human brain in response to afirst type of stimulus applied to the human brain, wherein the firstmodel represents a brain state of a human as a function of the firsttype of stimulus applied to the human brain, wherein constructing thefirst model comprises: scanning the brains of a plurality of testsubjects using functional magnetic resonance imaging (fMRI) to obtain atraining dataset of fMRI data while the first type of stimulus is beingapplied to the brains of the test subjects, wherein the training datasetof fMRI data represents neural activity in regions of the brains of thetest subjects in response to applied stimulus; processing the trainingdataset of fMRI data to form a set of model parameters, wherein at leastone model parameter of the set of model parameters is a dynamic modelparameter, wherein the dynamic model parameter is defined as a dynamicfunction of an applied stimulus such that the dynamic model parameterchanges based on a type of the applied stimulus, wherein the dynamicmodel parameter is trained based on a type of the applied stimulus usedto obtain the training dataset of fMRI data, wherein the dynamic modelparameter comprises at least one coefficient that dynamically changeswith time based on (i) a dependency of the dynamic model parameter onthe type of the applied stimulus and (ii) a time-dependency of theapplied stimulus; using the set of model parameters to form the firstmodel, such that the first model is configured to represent whichregions of a human brain are most predictive of at least one or morestimuli-dependent brain states of the human brain; wherein the modelcomprises a regression comprising coefficients, wherein the coefficientsof the regression are dependent upon the stimulus and expressed as aTaylor expansion of the stimulus, wherein the coefficients of theregression are dynamic model parameters of the set of model parameters,wherein the dynamic model parameters are indicated by βij(y) andexpressed as:βij(y)=α_(0ij)+α_(1ij) y+α _(2ij) y ²+ . . . ; wherein y represents thestimulus; and wherein α_(0ij), α_(1ij), and α_(2ij) are coefficients ofthe Taylor expansion and i and j are indexes of the parameters;utilizing the first model to determine a brain state of an individual,wherein utilizing the model comprises: acquiring a test dataset of fMRIdata for the individual by (i) applying the first type of stimulus tothe brain of the individual and (ii) obtaining fMRI data measurementsfrom the brain of the individual in response to the applied stimulus;and applying the acquired test dataset of fMRI data of the individual tothe first model to determine a subset of voxels of the first model whichis selected in response to the acquired test dataset of fMRI data,wherein the subset of voxels corresponds to a specific region of thehuman brain; determining that the individual has a brain state whichcorresponds to the human brain state represented by the first model,when the selected subset of voxels of the first model corresponds to anexpected subset of voxels of the first model which would be expected tobe selected in response to the applied test dataset of fMRI data if theindividual had said brain represented by the first model; wherein thehuman brain state represented by the first model comprises at least oneof a cognitive state and a mental disease state; and constructing asecond model which represents a pattern of neural activity that occursin regions of a human brain in response to a second type of stimulusapplied to the human brain, wherein second model represents a brainstate of a human as a function of the second type of stimulus applied tothe human brain, wherein the second model is constructed by dynamicallyadjusting the at least one dynamic model parameter of the set of modelparameters used to form the first model using a second training datasetof fMRI data which is acquired with the second type of stimulus beingapplied to the brains of the test subjects.